Local unitary symmetries of hypergraph states

Abstract

Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation and quantum error correction. The study of hypergraph states, with their richer multipartite entanglement and other nonlocal properties, has a promising outlook for new insight into multipartite entanglement. We present results analyzing local unitary symmetries of hypergraph states, including both continuous and discrete families of symmetries. In particular, we show how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed.

arXiv comment29 pages, 12 figures, version 2 corrects several typos, corrects statement of Proposition 7.16, updates several references

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• Verified measurement-based quantum computing with hypergraph states
• Extreme violation of local realism in quantum hypergraph states
• Graph states and local unitary transformations beyond local Clifford operations
• Entanglement of random hypergraph states
• Qudit hypergraph states and their properties
• Analysis of quantum error correction with symmetric hypergraph states
• Local Pauli stabilizers of symmetric hypergraph states
• Local unitary classes of states invariant under permutation subgroups
• Some Ulam's reconstruction problems for quantum states
• Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Quantum computation by teleportation and symmetry
• Multiple multi-control unitary operations: implementation and applications
• Multipartite entanglement sudden death and birth in randomized hypergraph states
• Finite-Function-Encoding Quantum States
• Randomized hypergraph states and their entanglement properties